In an experimental performance of a single throw of a pair of unbiased normal dice, three events E 1 , E 2 & E 3 are defined as follows:
E 1 : getting a prime numbered face on each dice
E 2 : getting the same number on each dice
E 3 : getting a sum total of dots on two dice equal to 8. Then:
Text Solution
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(b,d)E 1 = {(2, 2), (2, 3), (2, 5), (3, 2), (3, 3), (3, 5), (5, 2), (5, 3), (5, 5)}
E 2 = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)} ; E 3 = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}
E 1 ∩ E 2 ∩ E 3 = φ
E 1 ∩ E 2 ≠ φ ⇒ E 2 ∩ E 3 ≠ φ ⇒ E 1 ∩ E 3 ≠ φ
P(E 1 ∩ E 2 ) = 
= 
⇒ P(E 1 ).(E 2 ) = 
⇒ P(E 1 ∩ E 2 ) ≠ P(E 1 ) P(E 2 )
E 1 E 2 are not independent.
P 
= 
= 
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